CSKA's stylish win provided a timely boost for Leonid Slutsky's side ahead of their final Champions League group game.
Zenit St Petersburg's hopes of winning their fifth Russian Premier League title suffered a slight setback though as they were held to a goalless draw at Rostov.
The result left Zenit in second, two points adrift of league leaders Spartak, who face Rubin Kazan on Monday in their last match before the long Russian winter break.
CSKA's stylish win provided a timely boost for Leonid Slutsky's side ahead of their final Champions League group game against Spurs on Wednesday.
The Russians are bottom of Group E on three points, one behind Tottenham, as the two vie for a place in the Europa League accorded to the third-placed finishers.
Ivorian striker Lacina Traore put the former Red Army side 1-0 up in the 25th minute when he fired past Ural keeper Nikolai Zabolotny off a backheel pass by Zoran Tosic through a crowd of legs.
Ten minutes later Traore netted his second of the match before Israeli international Bibras Natcho scored from the spot, while 18-year-old forward Fedor Chalov rounded off the scoring in the 40th minute.
"In general I'm pleased with my team's performance this year taking into consideration our personnel problems," Slutsky said.
"We're not too far behind the leading duo and I believe we still have a decent chance to improve our position in the table after the winter break."
In Saint Petersburg, the opening period provided little in the way of goalmouth action.
Zenit's only meaningful chance came in the 11th minute when forward Artem Dzyuba failed to find the target after a corner kick while he was just four yards out.
Slovak international Robert Mak also squandered a clear chance just past the hour mark when he blazed over the crossbar from just outside the six-yard box.
"I'm pleased with my team's performance as we've done a tremendous amount of work today," Zenit's Romanian manager Mircea Lucescu said.
"We dominated the play, we created a number of chances but just failed to score. But we played well anyway."